We analyze daily death registry data for a sample of 1,161 Italian municipalities in the 7 regions most severely hit by COVID-19. Daily deaths almost tripled in the first thirty days since the onset. Overall, COVID-19 might have killed 0.1% of the local population in just forty days. We also find that the incidence of COVID-19 is hugely underreported in official statistics, perhaps by a factor of three. In terms of epidemic management, we find that the strategy of mass testing, at-home care provision and contact tracing, embraced by the Veneto region, might have contributed to significantly reduce the lethality of COVID-19. We estimate the effect of COVID-19 on mortality to be six times larger in Lombardia than in Veneto.